Digital linearizing system

ABSTRACT

A method of compensating for nonlinear distortions in a digital signal comprises receiving the digital signal, generating a nominal phase shifted signal based on the digital signal, generating a modeled distortion signal based on the digital signal and the nominal phase shifted signal, subtracting the modeled distortion signal from the digital signal, and generating a compensated signal. A compensating system comprises an input interface configured to receive a digital signal having nonlinear distortion, and a distortion model coupled to the interface, configured to generate a nominal phase shifted signal based on the digital signal, generate a modeled distortion signal based on the digital signal and the nominal phase shifted signal, subtract the modeled distortion signal from the digital signal, and generate a compensated signal.

CROSS REFERENCE TO OTHER APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 60/556,550 (Attorney Docket No. OPTIP008+) entitled DIGITALLINEARIZING SYSTEM filed Mar. 25, 2004, which is incorporated herein byreference for all purposes.

BACKGROUND OF THE INVENTION

In signal processing systems, there is often a need to compensate fornonlinear distortions introduced by the system. There are many possiblesources for system nonlinearities, including characteristics ofnonlinear components such as inductors, capacitors and transistors.Nonlinearities are frequently introduced when analog signals areconverted to digital. Besides component nonlinearities,analog-to-digital converters (ADCs) often have additional sources ofnonlinearity, such as the sampling capacitors' time constants, gainerror in amplifiers and imprecision in the comparator levels.

Nonlinear distortions may depend on many factors such as the inputsignal's frequency range, history and rate of change (also referred to“slew rate”), as well as external factors such as operating temperature.The difficulties in modeling nonlinear distortions lead to difficultiesin characterizing and compensating system nonlinearities. Existingtechniques for characterizing system nonlinearities such as Volterraexpansion tend to be complex and difficult to implement.

Furthermore, in some systems, even if a distortion model is found byusing Volterra expansion, it could not be accurately applied due to theunavailability of the required inputs. For example, in somecommunication systems, the receiver circuitry may introducenonlinearities when the input analog signal is digitized and demodulatedto baseband. The intermediate frequency (IF) signal required by thedistortion model is often unavailable since the IF signal is directlydemodulated to baseband when the ADC samples the signal. Applying thebaseband signal to the distortion model usually means that some of thehistory and slew rate information is lost; therefore, the distortionestimation is less accurate.

It would be useful to have a way to better compensate for systemnonlinearities even as some of the data required by the distortion modelis not available as input. It would also be useful if the compensationscheme could be applied without requiring special data access.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of the invention are disclosed in the followingdetailed description and the accompanying drawings.

FIGS. 1A-1C are diagrams illustrating several linearizer embodiments.

FIG. 2 is a flow chart illustrating an embodiment of a process forcompensating for nonlinear distortion in a digital signal.

FIGS. 3A-3C are signal diagrams illustrating the processing of abaseband signal according to some linearizer embodiments.

FIGS. 4A-4D are diagrams illustrating the processing of an input signalwithin a higher order Nyquist zone.

FIG. 5 is a block diagram illustrating a linearizer embodiment.

FIG. 6 is a block diagram illustrating the implementation of a linearprocessing module embodiment.

FIG. 7 is a diagram illustrating another linear processing moduleembodiment.

FIG. 8 is a diagram illustrating another linear processing moduleembodiment.

FIG. 9 is a block diagram illustrating a nonlinear processor embodiment.

DETAILED DESCRIPTION

The invention can be implemented in numerous ways, including as aprocess, an apparatus, a system, a composition of matter, a computerreadable medium such as a computer readable storage medium or a computernetwork wherein program instructions are sent over optical or electroniccommunication links. In this specification, these implementations, orany other form that the invention may take, may be referred to astechniques. A component such as a processor or a memory described asbeing configured to perform a task includes both a general componentthat is temporarily configured to perform the task at a given time or aspecific component that is manufactured to perform the task. In general,the order of the steps of disclosed processes may be altered within thescope of the invention.

A detailed description of one or more embodiments of the invention isprovided below along with accompanying figures that illustrate theprinciples of the invention. The invention is described in connectionwith such embodiments, but the invention is not limited to anyembodiment. The scope of the invention is limited only by the claims andthe invention encompasses numerous alternatives, modifications andequivalents. Numerous specific details are set forth in the followingdescription in order to provide a thorough understanding of theinvention. These details are provided for the purpose of example and theinvention may be practiced according to the claims without some or allof these specific details. For the purpose of clarity, technicalmaterial that is known in the technical fields related to the inventionhas not been described in detail so that the invention is notunnecessarily obscured.

A method and system for compensating nonlinear distortion in a digitalsignal is disclosed. In some embodiments, a nominal phase shifted signalis generated based on the digital signal. A modeled distortion signal isgenerated based on the digital signal and the nominal phase shiftedsignal and then subtracted from the digital signal. A compensated signalis then generated. A digital signal may result from an analog inputrestricted to a known region of operation (such as a Nyquist zone). Insome embodiments, the nominal phase shifted signal is generated byinterpolating the digital signal and taking interpolated values atfractional intervals of the sampling period of the digital signal. Insome embodiments, the nominal phase shifted signal is generated byup-sampling the digital signal, filtering the up-sampled signal andobtaining interpolated values at fractional intervals of the samplingperiod. A derivative calculated based on the digital signal and/or thenominal phase shifted signal may also be used by the distortion model. Acompensating system comprising a distortion model may be configured tocorrect for nonlinear distortions in analog to digital converters,receiver circuits, or any other appropriate system with nonlineardistortion in its channel.

FIGS. 1A-1C are diagrams illustrating several linearizer embodiments. InFIG. 1A, the output of nonlinear system 102 is sent to linearizer 104,which is configured to compensate for output distortion. The linearizercan be implemented as software or firmware code embedded in a processor,a field programmable date array (FPGA), a programmable digital signalprocessing (DSP) engine, an application specific integrated circuit(ASIC), any other appropriate device or combinations thereof. In thisexample, output 106 is treated as an ideal undistorted component plus adistortion component. The distortion component is separate from ADCquantization error, which is equal to the portion of the analog signalbelow the finest ADC quantization level and typically cannot be reducedfor an ADC with a predefined number of bits. The distortion component isto be predicted and corrected by linearizer 104. As will be shown inmore details below, linearizer 104 is configured to model the distortioncomponent using output 106 of the nonlinear system.

FIG. 1B is a block diagram of a receiver circuit embodiment thatincludes a linearizer. In this example, an analog radio frequency (RF)signal is received by radio frequency receiver 112. The signal isdemodulated to an IF signal by filter 114, and the IF signal is thenamplified by amplifier 116. The signal is converted to digital by ADC118. Linearizer 120 is configured to compensate for nonlinear distortionin digital signal 122 that results from component nonlinearities inreceiver chain. Similar to signal 106 of FIG. 1A, signal 122 is treatedas if it includes an ideal ADC output component and a distortioncomponent. The linearizer estimates the distortion based on digitalsignal 122 and generates a compensated output.

In FIG. 1, linearizer 120 is trained to model the nonlinear distortionintroduced by the entire receiver chain. A similar linearizer may alsobe used to compensate for nonlinearities in individual components. Forexample, in FIG. 1C, linearizer 134 is coupled to ADC 132 and isconfigured to compensate for the nonlinear distortions in the ADC. Forpurposes of illustration, ADC 132 is treated as the equivalent of anideal analog-to-digital converter 136 that generates an ideal digitalsignal 138, and a distortion module 140 that produces a distortioncomponent 142. The transfer function of the distortion module may benonlinear and varies with input signal 144, its history and its slewrate.

FIG. 2 is a flow chart illustrating an embodiment of a process forcompensating for nonlinear distortion in a digital signal. For purposesof illustration, the following examples discuss in detail the operationsand implementations of various linearizer embodiments that compensatefor distortion resulting from ADCs. The techniques are also applicableto distortion compensation in transceiver circuits or other appropriatesignal processing devices.

In this example, process 200 may be implemented on linearizers 104, 120,134 or other appropriate devices. The process begins when a digitalsignal is received (202). The digital signal may be the result of ananalog-to-digital converter such as ADC 132 of FIG. 1C. One or morenominal phase shifted signals based on the digital signal are thendetermined (204). The samples in a nominal phase shifted signalcorrespond to the samples of the ADC input at fractional sampling phasesof the digital signal (in other words, samples at fractional intervalsbetween the sampling periods of the ADC). As will be shown in moredetails below, the nominal phase shifted signal may be generated usingtechniques such as interpolation, upsampling, direct modulation, or anyother appropriate technique. The received digital signal and the nominalphase shifted signal are processed by a distortion module to generate amodeled distortion signal (206). The modeled distortion signal is thensubtracted from the digital signal to generate a compensated signal(208).

Process 200 may be illustrated using the system embodiment shown in FIG.1C. ADC output 152 corresponds to the received digital signal (202).Nominal phase shifted signals based on the digital signal is determinedby system distortion model 146 (204). The digital signal and the nominalphase shifted signals are processed to generate a modeled distortionsignal that is approximately equal to distortion signal 142 (206).Estimated distortion 148 is then subtracted from output 152 of ADC 132to generate a compensated signal 150.

In some embodiments, the linearizer generates nominal phase shiftedsignals based on the digital signal received. In some embodiments, thelinearizer also generates derivatives based on the nominal phase shiftedsignals. The nominal phase shifted signals and/or the derivatives areused by the system distortion model. FIGS. 3A-3C are signal diagramsillustrating the processing of a baseband signal according to somelinearizer embodiments. FIG. 3A is a frequency spectrum diagramillustrating a baseband digital signal 300. In this example, a basebandanalog signal is sampled and filtered to produce baseband digital signal300, therefore the sampling of the baseband analog signal does not havedemodulating effects. Signal 300 is shown to include several frequencycomponents. Signal component 302 is the ideal digital signal componentwithout nonlinear distortion. Signals 304 and 306 are the distortioncomponents.

The discrete samples of signal 300 in the time domain are shown in FIG.3B. The samples can be interpolated to reconstruct a signal thatcorresponds to the original baseband analog signal. FIG. 3C shows theinterpolated signal 320. Nominal phase shifted samples at fractionalphases of the ADC's sampling phase are generated according tointerpolated signal 320. In the example shown, for an ADC with asampling period of T, the nominal phase shifted samples are generated attimes T+ξ, T+2ξ, . . . , T+nξ, 2T+ξ, 2T+2ξ, . . . , 2T+nξ, etc., where ξis a fractional value of T. The nominal phase shifted samples and theoriginal samples are sent to the distortion model as inputs. In theexample shown, the distortion model depends on the history of the inputsamples and the derivatives of the input. The nominal phase shiftedsamples provide enhanced history information, and the derivativesprovide information about the signals rate of change. The additionalinformation allows the distortion model to more accurately compute theresulting distortion signal.

In some embodiments, the input frequencies are restricted to a specificregion. The distortion model can produce better modeled distortionsignal if the frequency region is known. In the examples below, inputsrestricted to specific frequency regions referred to as Nyquist zonesare discussed in detail. As used herein, the n-th Nyquist zone spans thefrequency range between${\frac{( {n - 1} )}{2}f_{s}\quad{to}\quad\frac{n}{2}f_{s}},$where f_(s) is equal to the ADC's sampling frequency. The technique isalso applicable to other types of frequency bands.

FIGS. 4A-4D are diagrams illustrating the processing of an input signalwithin a higher order Nyquist zone. FIG. 4A is a frequency spectrumdiagram illustrating the input signal. Input 402 is sampled to generatean aliased image 404 in the baseband. FIG. 4B is a time domain diagramillustrating input signal 402 and aliased baseband signal 404. Thebaseband signal includes samples such as 412 and 414. As shown in thisdiagram, certain information contained in input signal 402, such as datahistory and rate of change, is not captured by the baseband samples.Although the original signal 402 is not available to the distortionmodel in this example, some of the missing information can be recreatedby digitally modulating baseband signal 404 to the Nyquist zone wherethe analog signal originated. In some embodiments, the digitalmodulation is done directly by multiply the baseband signal with acarrier frequency. In some embodiments, the digital modulation isachieved by upsampling the baseband signal.

In FIG. 4C, the baseband signal is upsampled. Zeros are inserted whereno sample value is available. The upsampling rate R may vary fordifferent embodiments. The choice of R depends on several factors. Oneof the factors is the ratio of the integral sampling period and therequired fractional phase. The upsampling rate should be greater thanthis ratio. For example, for an integral sampling period of T, if thefractional phase ξ is 0.1 T, then the upsampling rate should be greaterthan 1/0.1=10. The upsampling rate also depends on the spectrum of theADC's input signal. In sub-sampling applications, the input signal maybe at a higher frequency than the ADC sampling rate. In theseapplications R is chosen to be equal to the sub-sampling rate times1/(ξ/T). For example, if the ADC's sampling rate is 100 MHz, and theinput signal lies between 150 MHz and 200 MHz, then the sub-samplingrate is 4. This is because 0-50 MHz is the frequency range of the firstNyquist zone, and 150-200 MHz is 4-times higher. If the desired ξ/T=0.1,then the upsampling rate R=4/0.1=40. The upsampled signal isinterpolated and band-pass filtered to reconstruct the signal at anappropriate frequency. The nominal phase shifted signals are thenobtained at the desired fractional phase as shown in FIG. 4D.

FIG. 5 is a block diagram illustrating a linearizer embodiment. In thisexample, linearizer 500 includes a linear processing module 502 coupledwith a nonlinear processing module 504. Linear processing module 502 isconfigured to estimate the nominal phase shifted symbols such asy_(n-ξ)and y_(n-2ξ), and derivates such as {dot over (y)}_(n) , {dotover (y)}_(n-ξ)and {dot over (y)}_(n-2ξ). Nonlinear processing module504 is configured to implement the distortion model that estimates thedistortion based on the digital samples, the nominal phase shiftedsamples and the derivates.

FIG. 6 is a block diagram illustrating the implementation of a linearprocessing module embodiment. In this example, linear processing module502 includes an upsampling module 602 that upsamples digital input y_(n)at a rate of R. Returning to signal examples shown in FIGS. 4B-4D, inputy_(n) corresponds to the samples shown in FIG. 4B. The output ofup-sampling module 602 corresponds to the signal shown in FIG. 4C.Upsampling generates several images of the baseband input signal indifferent frequency regions. A plurality of digital filters such asdigital filter 604 is used to select an image in an appropriatefrequency region. In this example, the selected image is located in thesame Nyquist zone as the original analog signal that is digitized. Thus,the characteristics of filter bank depend on the desired Nyquist zone.Low-pass, band-pass and high-pass digital filters may be used to achievethe desired filter characteristics.

The outputs of the digital filters are down-sampled by down-samplerssuch as 606. During the down-sampling operation, each down-samplerselects samples that correspond to a desired phase. FIG. 4D illustratesthe results of phase selection according to one embodiment. In theexample shown, samples 410 a, 410 b, 410 c, 410 d, etc. that correspondto phase 1 are selected to form a nominal phase shifted signal y_(n-ξ).Similarly, samples 412 a, 412 b, 412 c, 412 d, etc. that correspond tophase 2 are selected to form a nominal phase shifted signal y_(n-2ξ).The difference between two adjacent phase signals is computed by adifferencing module such as 608. Derivatives such as {dot over (y)}_(n),{dot over (y)}_(n-ξ)and {dot over (y)}_(n-2ξ) are computed based on thedifference.

FIG. 7 is a diagram illustrating another linear processing moduleembodiment. In this example, the input signal y_(n) is directly sent toa plurality of digital filters without up-sampling. The digital filtersused in this example are decimated versions of the digital filters usedin FIG. 6. For a given digital filter, the decimation is chosen at anappropriate phase to yield a filter output that corresponds to a nominalphase shifted signal. The differences between filter outputs of adjacentphases provide derivative estimates.

FIG. 8 is a diagram illustrating another linear processing moduleembodiment. In this example, two adjacent phase digital filters andtheir corresponding differencing modules are combined into a digitalHilbert filter. The Hilbert filter has an impulse response that isequivalent to the difference in the impulse responses of digital filtershaving adjacent phases. The output of the digital Hilbert filterprovides a direct estimate of the signal derivative at the desiredphase.

FIG. 9 is a block diagram illustrating a nonlinear processor embodiment.In this example, nonlinear processor 900 implements the distortion modelof the ADC. The transfer function of the distortion model may be derivedby sending test inputs with different amplitudes and varying slew ratesto the ADC. In some embodiments, the nonlinear transfer function of thedistortion model can be expressed as the following general form:{circumflex over (η)}_(n) ã _(0,n)(Y _(n))y _(n) +. . . +ã _(2N-2,n)(Y_(n))y _(n-2N+2) +{tilde over (b)} _(n)(Y _(n))   (Equation 1).where Y_(n) is a vector including the integral samples, the fractionalsamples, and the derivatives. An example of Y_(n) isY _(n) =|y _(n) y _(n-ξ) y _(n-2ξ) {dot over (y)} _(n) {dot over (y)}_(n-ξ) {dot over (y)} _(n-2ξ) y _(n-1) y _(n-2) y _(n-3)].

Equation 1 can be viewed as a “linear” convolution between the inputvariables and the nonlinear coefficients that are time variant nonlinearfunctions of the input signal. In other words, the function has the formof a linear filter, but with nonlinear coefficients. The relativelocation of input Y_(n) in the multi-dimensional input space determinesthe values of the ã_(j,n) and {tilde over (b)}_(n) coefficients. Thedependence of the filter coefficient values on the input signal vectorgives the filter its nonlinear property.

The nonlinear processor output, {circumflex over (v)}_(n), includes areplica of the original linear signal v_(n) and the residual uncorrectednonlinear distortion {tilde over (η)}_(n). The relationship may beexpressed as:{tilde over (v)} _(n) =y _(n)−{circumflex over (η)}_(n) =v_(n)+η_(n)−{circumflex over (η)}_(n) =v _(n)+{tilde over (η)}_(n)  (equation 2), where{tilde over (η)}_(n)=η_(n)−{tilde over (η)}hd n. (equation 3).

In some embodiments, a distortion model similar to equation 1 can beimplemented using one or more minimum-maximum processors and/or absolutevalue processors. Details of the implementation are described in U.S.Pat. No. 6,856,191,entitled NONLINEAR FILTER, which is incorporatedherein by reference for all purposes. According to the techniquesdescribed, the transfer function of the distortion model may beexpressed as: $\begin{matrix}{{\hat{\eta}}_{n} = {{A^{T}Y_{n}} + b + {\sum\limits_{j = 1}^{K}{c_{j}{{{{{\overset{->}{\alpha}}_{j}Y_{n}} + \beta_{j}}}.}}}}} & ( {{equation}\quad 4} )\end{matrix}$

Let sign ({right arrow over (α)}_(j)Y_(n)+β_(j))=λ_(jn), equation 4 canbe rewritten as: $\begin{matrix}{{\hat{\eta}}_{n} = {{( {a_{0} + {\sum\limits_{j = 1}^{K}{c_{j}\alpha_{0j}\lambda_{jn}}}} )y_{n}} + \cdots + {( {a_{N} + {\sum\limits_{j = 1}^{K}{c_{j}\alpha_{N,j}\lambda_{jn}}}} )y_{n - N}} + {( {b + {\sum\limits_{j = 1}^{K}{c_{j}\beta_{j}\lambda_{jn}}}} ).}}} & ( {{equation}\quad 5} )\end{matrix}$Equation 5 is also equivalent to equation 1.

The distortion function may be transformed into vector form to simplifythe function and achieve computational reductions. In some embodiments,the distortion function is implemented as a low complexity filter withreduced number of multiplication operations. The distortion function ofequation 4 can be transformed as follows: $\begin{matrix}\begin{matrix}{{\hat{\eta}}_{n} = {{A^{T}Y_{n}} + b + {\sum\limits_{j = 1}^{K_{1}}{c_{j}{{y_{n} + \beta_{j}}}}} +}} \\{{\sum\limits_{j = {K_{1} + 1}}^{K_{2}}{c_{j}{{y_{n - 1} + \beta_{j}}}\quad\cdots}} + {\sum\limits_{j = {K_{{2N} - 3} + 1}}^{K_{{2N} - 2}}{c_{j}{{y_{n - N} + \beta_{j}}}}}} \\{= {{A^{T}Y_{n}} + b + {\sum\limits_{j = 1}^{K_{1}}{c_{j}{\lambda_{j,n}( {y_{n} + \beta_{j}} )}}} +}} \\{{\sum\limits_{j = {K_{1} + 1}}^{K_{2}}{c_{j}{\lambda_{j,n}( {y_{n - 1} + \beta_{j}} )}\quad\cdots}} +} \\{\sum\limits_{j = {K_{{2N} - 3} + 1}}^{K_{{2n} - 2}}{c_{j}{{\lambda_{j,n}( {y_{n - N} + \beta_{j}} )}.}}}\end{matrix} & ( {{equation}\quad 6} )\end{matrix}$Let λ_(j,n)=sign (y_(n-1)+β_(j)), the function can be furthertransformed as $\begin{matrix}{{\hat{\eta}}_{n} = {{( {a_{0} + {\sum\limits_{j = 1}^{K_{1}}{c_{j}\lambda_{jn}}}} )y_{n}} + \cdots + {( {a_{{2n} - 2} + {\sum\limits_{j = {K_{{2N} - 3} + 1}}^{K_{{2N} - 2}}{c_{j}\lambda_{jn}}}} )y_{n - N}} + {( {b + {\sum\limits_{j = 1}^{K}{c_{j}\beta_{j}\lambda_{jn}}}} ).}}} & ( {{equation}\quad 7} )\end{matrix}$

A filter implementing the general form of equation 7 is referred to as afirst order nonlinear filter since each coefficient is multiplied withterms of y to the first order at most. In some embodiments, c_(j) andc_(j)β_(j) are pre-computed and stored. Since λ_(jn) is either 1 or −1,the coefficients can be computed without using multiplication and thecomplexity in filter implementation is greatly reduced.

Other simplifications using vector manipulation are also possible. Forexample, another simplified form of the distortion function is expressedas:{tilde over (η)}_(n) f _(0,n)(Y _(n))y _(n) +. . . +f _(2N-2,n)(Y _(n))y_(n-2N+2) +ã _(0,n)(Y _(n))y _(n) +. . . ã _(2N-2,n)(Y _(n))y _(n-2N+2)+{tilde over (b)} _(n)(Y _(n))   (equation 8),where each f_(k,n) (Y_(n)) is a first order nonlinear function$\begin{matrix}\begin{matrix}{{f_{k,n}( Y_{n} )} = {{A_{k}^{T}Y_{n}} + b_{k} + {\sum\limits_{j = 1}^{K}{c_{j}^{k}{{{{\overset{->}{\alpha}}_{j}^{k}Y_{n}} + \beta_{j}^{k}}}}}}} \\{= {{{{\overset{\sim}{a}}_{0,n}^{k}( Y_{n} )}y_{n}} + \cdots + {{{\overset{\sim}{a}}_{{{2N} - 2},n}^{k}( Y_{n} )}y_{n - {2N} + 2}} +}} \\{{{\overset{\sim}{b}}_{n}^{k}( Y_{n} )}.}\end{matrix} & ( {{equation}\quad 9} )\end{matrix}$Accordingly, each coefficient in equation 8 is a nonlinear function ofthe input vector elements and some of the coefficients multiply apower-of-two element of the input vector or cross-product-of-twoelements of the input vector. A filter implementing this simplified formis referred to as a second order filter.

In some embodiments, the distortion function is simplified to haveconstants in each discrete input region. This simplification results ina zero order transfer function. The zero order filter is sometimesreferred to as a “catastrophic” structure because of the discontinuitiesin the filter response. A general form of a zero order nonlinear filteris expressed as: $\begin{matrix}{{\hat{\eta}}_{n} = {a_{0} + a_{1} + \ldots + a_{{2N} - 2} + b + {\sum\limits_{j = 1}^{K}{c_{j}^{0}\lambda_{j}^{0}}} + {\sum\limits_{j = 1}^{K}{c_{j}^{1}\lambda_{j}^{1}}} + \ldots + {\sum\limits_{j = 1}^{K}{c_{j}^{{2N} - 2}{\lambda_{j}^{{2N} - 2}.}}}}} & ( {{equation}\quad 10} )\end{matrix}$

To implement a zero order nonlinear filter, combinations of${\sum\limits_{j = 1}^{K}{c_{j}^{0}\lambda_{jn}^{0}}},{\sum\limits_{j = 1}^{K}{c_{j}^{1}\lambda_{jn}^{1}}},$etc. may be pre-computed, stored and retrieved based on the appropriateinput. In some embodiments, the coefficient value is determined using anindicator that indicates the relative location of the input within therange of possible inputs. The indicator is sometimes referred to as a“thermometer code,” which is a vector having a total of at most one signchange among any two adjacent elements.

Take the following second order function as an example: $\begin{matrix}\begin{matrix}{{\hat{\eta}}_{n} = {{a_{0}y_{n}} + {a_{1}y_{n - 1}} + b + {\sum\limits_{j = 1}^{K}{c_{j}^{0}{{y_{n} + \beta_{j}^{0}}}y_{n}}} +}} \\{\sum\limits_{j = 1}^{K}{c_{j}^{1}{{y_{n - 1} + \beta_{j}^{1}}}y_{n}}} \\{= {{( {\sum\limits_{j = 1}^{K}{c_{j}^{0}\lambda_{j}^{0}}} )y_{n}^{2}} + {( {\sum\limits_{j = 1}^{K}{c_{j}^{1}\lambda_{j}^{1}}} )y_{n}y_{n - 1}} +}} \\{{( {a_{0} + {\sum\limits_{j = 1}^{K}{c_{j}^{0}\lambda_{j}^{0}\beta_{j}^{0}}} + {\sum\limits_{j = 1}^{K}{c_{j}^{1}\lambda_{j}^{1}\beta_{j}^{1}}}} )y_{n}} + {a_{1}y_{n - 1}} + b} \\{= {{{\overset{\sim}{a}}_{01,n}y_{n}^{2}} + {{\overset{\sim}{a}}_{1,n}y_{n}y_{n - 1}} + {{\overset{\sim}{a}}_{0,n}y_{n}} + {a_{1,n}y_{n - 1}} + {b.}}}\end{matrix} & ( {{equation}\quad 11} )\end{matrix}$

The input is compared to the set of β_(j) ^(K) values to determine therelative location of the input variable within the range of possibleinputs, and the vector of λ_(j,n), denoted as Λ_(n). Depending on theinput, Λ_(n) may be a vector with terms that are +1 only, −1 only, or −1for the first k terms and +1 for the rest of the terms. In other words,Λ_(n) is a thermometer code with at most one sign change among itsterms. For example, assuming that constants β_(j) ^(K) are distributedacross the dynamic range of y_(n)ε(−1,1) and there are 8 values of${\beta_{j}^{k} \in {{{( {{- \frac{4}{7}} - \frac{3}{7} - \frac{2}{7} - {\frac{1}{7}\frac{1}{7}\frac{2}{7}\frac{3}{7}\frac{4}{7}}} ).\quad{If}}\quad y_{n}} < {- \frac{4}{7}}}},{then}$${\Lambda_{n} = {{{\lbrack {{- 1} - 1 - 1 - 1 - 1 - 1 - 1 - 1} \rbrack.\quad{If}}\quad y_{n}} > \frac{4}{7}}},{then}$Λ_(n) = [+1 + 1 + 1 + 1 + 1 + 1 + 1 + 1].If y_(n) is somewhere in between, Λ_(n) may have a sign change. Forexample, if${y_{n} = \frac{3.5}{7}},{{{then}\quad\Lambda_{n}} = {{{\lbrack {{- 1} - 1 - 1 - 1 - 1 - 1 - 1 + 1} \rbrack.{If}}\quad y_{n}} = \frac{1.5}{7}}},{\Lambda_{n} = {\lbrack {{- 1} - 1 - 1 + 1 + 1 + 1 + 1 + 1} \rbrack.}}$then Since the thermometer code has only 8 valves, there are only 8possible values for${{\overset{\sim}{a}}_{01,n} = {\sum\limits_{j = 1}^{K}\quad{c_{j}^{0}\lambda_{j}^{0}}}},$8 possible values for${{\hat{a}}_{1,n} = {\sum\limits_{j = 1}^{K}\quad{c_{j}^{1}\lambda_{j,n}^{1}}}},$and 64 possible values for${\overset{\sim}{a}}_{0,n} = {a_{0} + {\sum\limits_{j = 1}^{K}\quad{c_{j}^{0}\lambda_{j}^{0}\beta_{j}^{0}}} + {\sum\limits_{j = 1}^{K}\quad{c_{j}^{1}\lambda_{j}^{1}{\beta_{j}^{1}.}}}}$

The number of add operations can be reduced by pre-computing thepossible values for coefficients of ã_(01,n), â_(1,n), etc. and storingthem in memory. In this example, the addresses of the coefficients arestored in a lookup table, which stores the 8 possibilities ofthermometer code Λ_(n) and the corresponding addresses of pre-computedcoefficients. The coefficients can be retrieved by accessing the memoryaddresses that correspond to the appropriate thermometer code entry.Once the coefficients ã_(01,n), â_(11,n) etc. . . . are read out ofmemory, the filter output can be computed as{circumflex over (η)}_(n)=ã_(01,n) y _(n) ²+â_(1,n) y _(n) y _(n-1) +ã_(0,n) y _(n) +a _(1,m) y _(n-1) +b   (equation 12).This technique is also applicable to zero, first or higher orderfilters.

Low complexity nonlinear filters may be implemented based on thesimplified forms. In some embodiments, the low complexity linear filterincludes a processor coupled to the nonlinear filter, configured todetermine the relative location of the input variable within a range ofpossible inputs and to determine a filter coefficient of the nonlinearfilter using the relative location of the input variable. The filtercoefficients can be determined without using multiplication operations.In some embodiments, filter coefficients for zero order, first order,second order and/or higher order filters are pre-computed, stored andretrieved when appropriate. Higher order filters can be formed bynesting lower order filters. Details of implementing a nonlineartransfer function using low-complexity filter or thermometer code aredescribed in U.S. patent application Ser. No. 11/061,850 (AttorneyDocket No. OPTIP006) entitled LOW-COMPLEXITY NONLINEAR FILTERS, filedFeb. 18, 2005, which is incorporated herein by reference for allpurposes.

In some embodiments, the distortion model is temperature compensated.The coefficients of the distortion model at different temperatures arepredetermined and stored. During operation, the coefficientscorresponding to the operating temperature is selected to construct anappropriate distortion correction filter. In some embodiments, theoperating temperature is used to analytically determine thecorresponding coefficients. In other words, the coefficients arecomputed based on a function of the input and its history, thederivatives of the input, the temperature, the changes in temperature,any other appropriate factors or a combination thereof.

An improved method for compensating nonlinear distortions in digitalsignals and a linearizer system have been disclosed. Nonlinearities ofADCs, receivers, or other systems with nonlinear channel characteristicscan be more effectively compensated by modeling the nonlinearities usingthe digital signal, the nominal phase shifted signals, and theirderivatives.

Although the foregoing embodiments have been described in some detailfor purposes of clarity of understanding, the invention is not limitedto the details provided. There are many alternative ways of implementingthe invention. The disclosed embodiments are illustrative and notrestrictive.

1. A method of compensating for nonlinear distortions in a digitalsignal, comprising: receiving the digital signal; generating a nominalphase shifted signal based on the digital signal; generating a modeleddistortion signal based on the digital signal and the nominal phaseshifted signal; subtracting the modeled distortion signal from thedigital signal; and generating a compensated signal.
 2. A method asrecited in claim 1, wherein the digital signal results from an analoginput signal restricted to a known region of operation.
 3. A method asrecited in claim 1, wherein the digital signal results from an analoginput signal restricted to a specific Nyquist zone.
 4. A method asrecited in claim 1, wherein the digital signal includes an undistorteddigital component and a distortion component.
 5. A method as recited inclaim 1, wherein the digital signal includes an undistorted digitalcomponent and a distortion component, and the method further comprisesgenerating a modeled distortion signal that is a function of both theundistorted digital component and the distorted component.
 6. A methodas recited in claim 1, wherein generating the nominal phase shiftedsignal includes modulating the digital signal.
 7. A method as recited inclaim 1, wherein generating the nominal phase shifted signal includesinterpolating the digital signal and taking interpolated values atfractional intervals of a sampling period of the digital signal.
 8. Amethod as recited in claim 1, wherein generating the nominal phaseshifted signal includes up-sampling the digital signal to generate anup-sampled signal, filtering the up-sampled signal and obtaininginterpolated values at fractional intervals of a sampling period of thedigital signal.
 9. A method as recited in claim 1, wherein: the digitalsignal results from an analog input signal restricted to a known regionof operation; and generating the nominal phase shifted signal includes:up-sampling the digital signal to generate an up-sampled signal;filtering the up-sampled signal according to the known region ofoperation; and obtaining interpolated values at fractional intervals ofa sampling period of the digital signal.
 10. A method as recited inclaim 1, further comprising generating a derivative of the digitalsignal; wherein the modeled distortion signal is generated based on thedigital signal, the nominal phase shifted signal and the derivative ofthe digital signal.
 11. A method as recited in claim 1, furthercomprising generating a nominal phase shifted derivative of the digitalsignal; wherein the modeled distortion signal is generated based on thedigital signal, the nominal phase shifted signal and the nominal phaseshifted derivative to the distortion model.
 12. A method as recited inclaim 1, wherein the digital signal is generated by an analog-to-digitalconverter.
 13. A method as recited in claim 1, wherein the digitalsignal is generated by a radio frequency receiver.
 14. A compensatingsystem comprising: an input interface configured to receive a digitalsignal having nonlinear distortion; and a distortion model coupled tothe interface, configured to: generate a nominal phase shifted signalbased on the digital signal; generate a modeled distortion signal basedon the digital signal and the nominal phase shifted signal; subtract themodeled distortion signal from the digital signal; and generate acompensated signal.
 15. A compensating system as recited in claim 14,wherein the digital signal results from an analog input signalrestricted to a known region of operation.
 16. A compensating system asrecited in claim 14, wherein the digital signal results from an analoginput signal restricted to a specific Nyquist zone.
 17. A compensatingsystem as recited in claim 14, wherein the digital signal includes anundistorted digital component and a distortion component.
 18. Acompensating system as recited in claim 14, wherein the digital signalincludes an undistorted digital component and a distortion component,and the distortion model is further configured to generate a modeleddistortion signal that is a function of both the undistorted digitalcomponent and the distorted component.
 19. A compensating system asrecited in claim 14, wherein generating the nominal phase shifted signalincludes modulating the digital signal.
 20. A compensating system asrecited in claim 14, wherein generating the nominal phase shifted signalincludes interpolating the digital signal and taking interpolated valuesat fractional intervals of a sampling period of the digital signal. 21.A compensating system as recited in claim 14, wherein generating thenominal phase shifted signal includes up-sampling the digital signal togenerate an up-sampled signal, filtering the up-sampled signal andobtaining interpolated values at fractional intervals of a samplingperiod of the digital signal.
 22. A compensating system as recited inclaim 14, wherein: the digital signal results from an analog inputsignal restricted to a known region of operation; and generating thenominal phase shifted signal includes: up-sampling the digital signal togenerate an up-sampled signal; filtering the up-sampled signal accordingto the known region of operation; and obtaining interpolated values atfractional intervals of a sampling period of the digital signal.
 23. Acompensating system as recited in claim 14, further comprisinggenerating a derivative of the digital signal and inputting thederivative of the digital signal to the distortion model.
 24. Acompensating system as recited in claim 14, further comprisinggenerating a nominal phase shifted derivative of the digital signal andinputting the nominal phase shifted derivative to the distortion model.25. A compensating system as recited in claim 14, wherein the digitalsignal is generated by an analog-to-digital converter.
 26. Acompensating system as recited in claim 14, wherein the digital signalis generated by a radio frequency receiver.
 27. A compensating system asrecited in claim 14, wherein the digital signal is generated by anonlinear system having nonlinear channel characteristics.
 28. Acompensating system as recited in claim 14, wherein the distortion modelcomprises a linear processing module coupled with a nonlinear processingmodule.
 29. A compensating system as recited in claim 14, wherein thedistortion model comprises a linear processing module coupled with anonlinear processing module, and the linear processing module isconfigured to generate the nominal phase shifted signal and thenonlinear processing module is configured to implement a nonlineardistortion function.
 30. A compensating system as recited in claim 14,wherein the distortion model includes a low complexity filter configuredto implement a nonlinear distortion function.
 31. A compensating systemas recited in claim 14, wherein the distortion modeled implements anonlinear function that has a linear form with nonlinear coefficients.32. A compensating system as recited in claim 14, wherein the distortionmodeled implements a nonlinear function having a plurality ofcoefficients, and the plurality of coefficients are determined using athermometer code.
 33. A compensating system as recited in claim 14,wherein the distortion model is temperature compensated.
 34. A computerprogram product for compensating for nonlinear distortion in a digitalsignal, the computer program product being embodied in a computerreadable medium and comprising computer instructions for: receiving thedigital signal; generating a nominal phase shifted signal based on thedigital signal; generating a modeled distortion signal based on thedigital signal and the nominal phase shifted signal; subtracting themodeled distortion signal from the digital signal; and generating acompensated signal.